MCV4U
Name:
Date:
1.4 Practice
1. Sketch a function f (x) such that the following seven conditions are met:
--
a.
d.
lim f (x) = 2
x → −4 +
b.
lim − f ( x) = −1
c.
f (2) = 0
f.
x → −4
lim f ( x) = −2
e.
x→0
g.
f (−4) = −1
lim f ( x) = +∞
x → 3−
The domain of f (x) is {x ∈ R, x < 3}
Put as much detail into your graph as possible, given the seven conditions above.
g
8
Nov 2024
1.4 Limits and Continuity Practice
MCV4U
2. Evaluate each limit (on a separate piece of paper), if it exists.
a) lim
1 1
+
6 𝑥𝑥
𝑥𝑥→ −6 𝑥𝑥 + 6
b) lim
1 1
+
6 𝑥𝑥
𝑥𝑥→ −6 𝑥𝑥 − 6
c)
d)
e)
lim
𝑥𝑥→ +6 𝑥𝑥 − 6
lim
𝑥𝑥→4
lim1
𝑥𝑥→2
f)
g)
1 1
+
6 𝑥𝑥
lim
(7−𝑥𝑥)2 −9
4−𝑥𝑥
16𝑥𝑥 4 −1
2𝑥𝑥−1
3−√𝑥𝑥
𝑥𝑥→9 𝑥𝑥−9
√𝑥𝑥+7 − √7−𝑥𝑥
2𝑥𝑥
𝑥𝑥→0
lim
h) lim
16 − 𝑥𝑥
𝑥𝑥→16 √𝑥𝑥 − 4
i) lim
16 + 𝑥𝑥
𝑥𝑥→16 √𝑥𝑥 − 4
j)
lim
16 − 𝑥𝑥
𝑥𝑥→16 √𝑥𝑥 + 4
eeeeee
ANSWERS:
1
a) − 36
b) 0
c) DNE
d) 6
e) 4
1
f) − 6
1
g) 2√7
h) -8
i) DNE
j) 0
lim
9
↓